math f.2 20點..快

👨🏻‍🏫 學術台數學

ddobtn

2009-06-11 1:25 am

In the figure ,ABCDEFG is a heptagon formed by intetresting a regular n-gon and a regular 2n-gon.∠BAG and∠AGF are the interior angles of the regular n-gon,while ∠BCD, ∠CDE and ∠DEF are the interior angles of the regular 2n-gon.
(a)express ∠BAG in terms of n.
(b)express ∠BCD in terms of n.
(c)if (a) ∠ABC= ∠GFE=126 degree,find n.

圖.
http://hk.myblog.yahoo.com/ylf6b05/article?mid=36

更新1:

吾系好明...請解說..

回答 (1)

myisland8132

2009-06-11 1:45 am

✔ 最佳答案

(a) ∠BAG = 180(n-2)/n
(b) ∠BCD = 180(2n-2)/2n=180(n-1)/n
(c) The total degree of heptagon = 180*5=900
∠ABC= ∠GFE=126
So 2[180(n-2)/n]+3[180(n-1)/n]+2(126)=900
360(n-2)+540(n-1)=648n
252n=1260
n=5

2009-06-10 18:02:18 補充：
(c) part : 因為有兩個角∠BAG and∠AGF 是正n邊形的角﹐有三個角∠BCD, ∠CDE and ∠DEF 是正2n邊形的角。另兩個角是126﹐故得到上式。

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